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The Multi-Curve Potential Model

Author

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  • THE ANH NGUYEN

    (Department of Mathematics, University of Kaiserslautern, 67663 Kaiserslautern, Germany)

  • FRANK THOMAS SEIFRIED

    (Department IV – Mathematics, University of Trier, Universitätsring 19, 54296 Trier, Germany)

Abstract

We develop a general class of multi-curve potential models for post-crisis interest rates. Our model features positive stochastic basis spreads, positive term structures, and analytic pricing formulae for interest rate derivatives. Making a quanto interpretation of LIBOR lending transactions, we use a multi-currency analogy to model multiple term structures and formulate a general, tractable model of multiple term structures. As a special case of our approach, we obtain a rational lognormal model that extends the original Flesaker–Hughston (1996) rational lognormal model to a multi-curve setting. In this setting we obtain analytic pricing formulae for caps and swaptions.

Suggested Citation

  • The Anh Nguyen & Frank Thomas Seifried, 2015. "The Multi-Curve Potential Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(07), pages 1-32, November.
    • Handle: RePEc:wsi:ijtafx:v:18:y:2015:i:07:n:s0219024915500491
    DOI: 10.1142/S0219024915500491
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    References listed on IDEAS

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    1. N. Moreni & A. Pallavicini, 2014. "Parsimonious HJM modelling for multiple yield curve dynamics," Quantitative Finance, Taylor & Francis Journals, vol. 14(2), pages 199-210, February.
    2. Masaaki Fujii & Yasufumi Shimada & Akihiko Takahashi, 2009. "A Market Model of Interest Rates with Dynamic Basis Spreads in the presence of Collateral and Multiple Currencies," CARF F-Series CARF-F-196, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Apr 2011.
    3. Henrard, Marc, 2007. "The irony in the derivatives discounting," MPRA Paper 3115, University Library of Munich, Germany.
    4. Masaaki Kijima & Keiichi Tanaka & Tony Wong, 2009. "A multi-quality model of interest rates," Quantitative Finance, Taylor & Francis Journals, vol. 9(2), pages 133-145.
    5. Roberto Dieci & Xue-Zhong He & Cars Hommes (ed.), 2014. "Nonlinear Economic Dynamics and Financial Modelling," Springer Books, Springer, edition 127, number 978-3-319-07470-2, December.
    6. Constantinides, George M, 1992. "A Theory of the Nominal Term Structure of Interest Rates," The Review of Financial Studies, Society for Financial Studies, vol. 5(4), pages 531-552.
    7. Christa Cuchiero & Claudio Fontana & Alessandro Gnoatto, 2016. "A general HJM framework for multiple yield curve modelling," Finance and Stochastics, Springer, vol. 20(2), pages 267-320, April.
    8. St�phane Cr�pey & Zorana Grbac & Nathalie Ngor & David Skovmand, 2015. "A L�vy HJM multiple-curve model with application to CVA computation," Quantitative Finance, Taylor & Francis Journals, vol. 15(3), pages 401-419, March.
    9. Filipović, Damir & Trolle, Anders B., 2013. "The term structure of interbank risk," Journal of Financial Economics, Elsevier, vol. 109(3), pages 707-733.
    10. Naosuke Nakamura & Fan Yu, 2000. "Interest Rate, Currency and Equity Derivatives Valuation Using the Potential Approach," International Review of Finance, International Review of Finance Ltd., vol. 1(4), pages 269-294, December.
    11. L. C. G. Rogers, 1997. "The Potential Approach to the Term Structure of Interest Rates and Foreign Exchange Rates," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 157-176, April.
    12. Marek Rutkowski, 1997. "A note on the Flesaker-Hughston model of the term structure of interest rates," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(3), pages 151-163.
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    Cited by:

    1. Claudio Fontana & Zorana Grbac & Sandrine Gümbel & Thorsten Schmidt, 2020. "Term structure modelling for multiple curves with stochastic discontinuities," Finance and Stochastics, Springer, vol. 24(2), pages 465-511, April.
    2. Christa Cuchiero & Claudio Fontana & Alessandro Gnoatto, 2019. "Affine multiple yield curve models," Mathematical Finance, Wiley Blackwell, vol. 29(2), pages 568-611, April.
    3. Ernst Eberlein & Christoph Gerhart & Zorana Grbac, 2019. "Multiple curve Lévy forward price model allowing for negative interest rates," Post-Print hal-03898912, HAL.
    4. Andrea Macrina & Obeid Mahomed, 2018. "Consistent Valuation Across Curves Using Pricing Kernels," Papers 1801.04994, arXiv.org, revised Feb 2018.
    5. Markus Hess, 2020. "A pure-jump mean-reverting short rate model," Papers 2006.14814, arXiv.org.
    6. Thomas Krabichler & Josef Teichmann, 2020. "The Jarrow & Turnbull setting revisited," Papers 2004.12392, arXiv.org.

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